is it possible to have PCOS if your only symptom is not-very-often periods?
I would think so. PCOS has different levels of severity and displays in different symptoms. Me - I have excessive weight, irregular periods and get horrible hair on my face.

The best way to get an initial indication of whether you have PCOS is to ask for some type of glucose test. I forget the name of it but you have to go in, have a blood test, drink this gross stuff, wait an hour, have another blood test then wait an hour and have another blood test. This looks for whether you have increased testosterone, which is an indicator of PCOS. Another way to get diagnosed is to have a vaginal ultrasound, which will have a look at your ovaries.